Re: Squares and Pigeonhole Principle

Originally Posted by I-Think

Let S be a square region of side length 2. Show that among any 9 points in the square, there are 3 which form a triangle of area .

Consider a unit square, a square of side length one and area of one square unit.
Any three points from that unit square that do form a triangle,
The area of such a triangle is square units.Can you show that?

Now divide your given square into four sub-squares each of one square unit each.